This invention relates to the field of nuclear magnetic resonance (NMR) imaging and spectroscopy. NMR pulse sequences are sets of radio frequency pulses, gradient magnetic fields, and data acquisition schemes that define a particular NMR procedure. In NMR procedures, there are used a large number of different types of pulse sequences, each of which may have certain advantages in particular circumstances. NMR imaging and spectroscopy is most often performed with pulse sequences in which the raw data are samples of the multi-dimensional inverse Fourier transform of the desired image. These pulse sequences usually employ a data sampling grid that covers space in a rectangular pattern. By an appropriate choice of gradient magnetic fields and sampling timing, the data samples are obtained on a regular rectangular grid of points in what is known as k-space. By a rectangular grid is meant any grid in two or more dimensions whose lattice basis vectors form an orthogonal set. The vectors need not be of equal magnitude.
This rectangular grid is inefficient when the data is isotropically band-limited as it is when used in medical procedures. Moreover, pulse sequences for two, three and four-dimensional data sets are severely limited by the lengthy data acquisition process. NMR studies on clinical patients consist of several different pulse sequences and typically last an hour in order to produce an image of adequate diagnostic quality. This amount of time greatly increases the already high cost of the procedure, and if used on seriously ill patients, the patient may lack the tolerance necessary to complete the procedure. Therefore, the diagnostic quality of the procedure is often limited because of the reduced time involved. Moreover, system computer limitations on raw data storage and data throughput rates may also limit the type and quality of the procedures that may be performed.
As previously indicated, almost all currently know techniques acquire data in a rectangular sampling pattern. However, this sampling pattern is optimum only for imaging objects which completely fill a rectangular field of view. In medical applications, the images more nearly fill a circular field of view. Thus rectangular sampling is especially inefficient in these cases. Also, in medical applications the body cross-section being imaged frequently will extend in one direction beyond the selected field of view. When this happens, the image reconstruction algorithm produces an aliased image consisting of the parts that are out of the field of view superimposed on the normal image. This can make image interpretation difficult. Techniques exist that eliminate this problem by increasing the sampling density by acquiring twice as much data to give an actual field of view twice as large as the nominal value, but this greatly increases the time of the procedure. More efficient data sampling techniques are therefore desirable in order to reduce the number of data points required to be collected, and data points and time would be reduced if efficient sampling patterns were available and used. Achieving reduction in data points would thus speed the patient examination, improve the cost-effectiveness of the procedure and reduce the data storage and throughput requirements.
There is therefore a need for a ne method of data acquisition using more efficient sampling patterns and a new faster algorithm for computing the inverse discrete Fourier transform (IDFT) in these cases to perform the reconstruction for output pixels on a rectangular array. Such a new method must be capable of increasing the efficiency when used with most types of pulse sequences. Moreover, such a new method must be capable of producing an image of improved quality when the same amount of data and time are used with the more efficient sampling technique. In particular, there is a need for more efficent production of NMR images with higher spatial resolution.